Re: Can mind be a computation if physics is fundamental?

From: Bruno Marchal <>
Date: Fri, 14 Aug 2009 11:18:23 +0200

On 14 Aug 2009, at 03:21, Colin Hales wrote:

> Here's a nice pic to use in discussion.... from GEB. The map for a
> formal system (a tree). A formal system could not draw this picture.
> It is entirely and only ever 'a tree'. Humans dance in the forest.
> col

You may compare Hofstadter's picture with the Mandelbrot set, and
understand better why it is natural to think that the Mandelbrot set
(or its intersection with Q^2) to be a "creative set" in the sense of
Emil Post, that is, mainly, a (Turing) Universal system. The UD* (the
block comp multiverse) can be mapped in a similar way.

See here for a picture of the Mnadebrot set (and a comparison with
Verhulst bifurcation in the theory of chaos):

Or see here for a continuos enlargement:

Or perhaps better, in this context, a black and white enlargment:

or a 3-d version

Colors or eights help to see the border of the set, but it is really a
subset of R^2. The border is infinitely complex, but not fuzzy! It is
really a function from R^2 to {0, 1}.


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Received on Fri Aug 14 2009 - 11:18:23 PDT

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